a-4/7=1/(3a-1)

Solution for a-4/7=1/(3a-1) equation:

a-4/7=1/(3a-1)

We move all terms to the left:

a-4/7-(1/(3a-1))=0


Domain of the equation: (3a-1))!=0

a∈R


We calculate fractions


a+()/21a+(-12a)/21a=0

We multiply all the terms by the denominator


a*21a+(-12a)+()=0

We add all the numbers together, and all the variables

a*21a+(-12a)=0

Wy multiply elements

21a^2+(-12a)=0

We get rid of parentheses

21a^2-12a=0

a = 21; b = -12; c = 0;
Δ = b2-4ac
Δ = -122-4·21·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12}{2*21}=\frac{0}{42}
=0
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12}{2*21}=\frac{24}{42}
=4/7
$